We investigate macromolecular physical gels (strontium alginates) in a wide range of aging times and length scales by combining linear stress relaxation and dynamic light scattering (DLS) experiments. Stress relaxation shows an early logarithmic decay followed by a stretched exponential behavior, leading to define two characteristic times, which increase as distinct power laws of gel age. The DLS clearly displays anomalous microscopic dynamics, with compressed exponential decay of autocorrelation functions and ballistic wavelength dependence of the decay time. Thus, our results demonstrate that stretched stress relaxation can coexist with compressed intensity autocorrelation functions. In addition, comparison between rheology and DLS allows for the identification of two characteristic lengths that we interpret as the typical size of collapsing pores in the gel and of avalanche-like rearrangements. We discuss this scenario in terms of some recently proposed ideas on anomalous aging, such as ultralong-ranged dynamical correlations in closely athermal systems.